Typical Takagi-Sugeno and Mamdani fuzzy systems as universal approximators: necessary conditions and comparison

Abstract

Both Takagi-Sugeno (TS) and Mamdani fuzzy systems are known to be universal approximators. We investigate whether one type of the fuzzy approximators is more economic than the other type. We first establish necessary conditions on minimal system configuration of the typical TS fuzzy systems as function approximators. The resulting conditions reveal the strength of the TS fuzzy approximators, but the drawback is that a large number of fuzzy rules must be employed to approximate periodic or highly oscillatory functions. We then compare these necessary conditions with the ones that we established for the general Mamdani fuzzy systems in our previous papers (Ding et al. (1997)). Results of the comparison unveil that the minimal system configurations of the TS and Mamdani fuzzy systems are comparable. Our new findings are valuable in designing fuzzy systems, especially fuzzy controllers and models which are two most popular and successful applications of the fuzzy approximators.